Semiclassical symmetry of the Gross-Pitaevskii equation with quadratic nonlocal Hamiltonian

TL;DR

This paper explores the semiclassical symmetry properties of the Gross-Pitaevskii equation with a quadratic nonlocal Hamiltonian, linking symmetries of the linear and nonlinear forms to facilitate analysis.

Contribution

It establishes a connection between symmetry operators of the linear and nonlinear Gross-Pitaevskii equations with quadratic nonlocal Hamiltonians.

Findings

Reduced nonlinear problem to linear form

Identified relation between symmetry operators

Provided framework for symmetry analysis

Abstract

The Cauchy problem for the Gross--Pitaevsky equation with quadratic nonlocal nonlinearity is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear and nonlinear Gross--Pitaevsky equations is considered.